This invention relates to continuously variable transmissions and more particularly, it concerns an adjustable counterbalancing system for such transmissions in which torque is transmitted by friction to or from a body exhibiting inertial forces which vary with the speed ratio at which power is transmitted.
In commonly-assigned U.S. Pat. Nos. Re 29,328 and 4,152,946, several embodiments of continuously variable, mechanical power transmissions are disclosed in which three frame supported working bodies operate to transmit a mechanical power input to a rotatable output at infinitely variable output/input speed ratios within the design range of the transmission. For purposes of definition in this background discussion as well as in the ensuing detailed description of the present invention and in the appended claims, the three working bodies may be termed, respectively, an "alpha body" which is supported by the transmission frame to be concentric with a first axis, a "beta body" which is supported by the alpha body to be concentric with a second axis inclined with respect to and intersecting the first axis at a point of axes intersection, and an "omega body" carried by the frame to be concentric also with the first axis. Although any one of these three bodies may be rotatable on the respective axes with which they are concentric, one of the three is held against rotation to provide a reaction torque whereas the other two bodies are rotatable and coupled either directly or by gearing to the respective input and output shafting of the transmission.
It is to be noted that the terms "alpha body," "beta body" and "omega body" are completely arbitrary and as such, do not restrict the components designated thereby either to the class of transmission represented by the disclosure of the aforementioned application or to specific structure to be described hereinafter. The terms will, however, lend consistency of definition in the description to follow and facilitate an understanding of various speed relationships to be expressed by algebraic equations.
The continuously variable speed ratio capability of such transmissions is achieved by providing one of the beta and omega bodies with a pair of rolling or traction surfaces which are of revolution about the concentric body axis and which are of variable radii along that axis in symmetry with the point of first and second axes intersection. Physically, such rolling surfaces will thus provide the one body with a biconical-like configuration. The other of the beta and omega bodies is provided with a pair of rolling or traction surfaces which are also of revolution about the concentric body axis but which are of relatively constant radius. The pairs of rolling surfaces on the beta and omega bodies are retained in frictional engagement with each other at two contact points or zones capable of positional adjustment to vary the ratio of the beta body surface radius (R.sub.b) to the omega body surface radius (R.sub.w). Thus, if the alpha body is rotatable at a velocity (.alpha.) about the first axis, the rotational speed of the beta body about the second axis in a fixed frame of reference is (.beta.) and the rotational speed of the omega body on the first axis is (.omega.), then the respective speeds of the three bodies are related by the following equation: EQU .omega.-.alpha.+(.alpha.-.beta.)R.sub.b /R.sub.w =0. (1)
Because one of either the beta or the omega body extends within the other of such bodies, the radius ratio R.sub.b /R.sub.w may represent a value of either less than 1 (where R.sub.b is always less than R.sub.w) or more than 1 (where R.sub.b is always greater than R.sub.w). The function .rho. will be used hereinafter to designate either R.sub.b /R.sub.w or the reciprocal R.sub.w /R.sub.b, whichever is greater than 1, it being understood that .rho. or its reciprocal 1/.rho. are used appropriately.
In several of the transmission embodiments disclosed in the aforementioned U.S. patents, the normal force by which the rolling surfaces on the respective beta and omega bodies are retained in frictional contact is developed solely by an inertial couple tending to tilt the beta body into the omega body. In other embodiments, this normal force is developed mechanically such as by forcibly separating a pair of oppositely convergent conical members constituting the biconical beta or omega body, preferably under a force proportional to output torque. In these latter embodiments, the same inertial couple is deployed to oppose a rocking couple resulting from the mechanically developed normal force so that the loading on bearings due to the rocking couple is reduced or offset by the inertial couple.
The magnitude of the inertial couple in a given transmission design may be determined by the equation: EQU C1=[(I.sub.1 -I.sub.3).alpha..sup.2 sin .alpha. cos .alpha.]-[I.sub.3 .alpha.(.alpha.-.beta.) sin .alpha.]. (2)
In this equation, C1 is the inertial couple, I.sub.1 is the moment of inertia of the beta body relative to the second axis, I.sub.3 is the moment of inertia of the beta body relative to an axis perpendicular to the second axis at the point of axes intersection and .alpha. is the angle at which the first and second axes intersect. The remaining functions in equation (2) are the same as those used in equation (1).
If it is assumed that the transmission is operated at a constant input speed .alpha. and that in the transmission, the angle .alpha. is fixed, then the first bracketed function on the right side of equation (2) is constant. As such, that portion of the inertial couple attributed to this function may be precisely counterbalanced by an appropriate fixed distribution of mass in the alpha body. Also, the second bracketed function in equation (2) may be constant in transmission designs in which the beta body is retained against rotation on the second axis so that .beta.=0. Such transmission designs are disclosed in U.S. Pat. No. 4,152,946 and operate to transmit power from the alpha body to the omega body, the latter being the output of the transmission and variable in accordance with the equation: EQU .omega.=.alpha.(1-.rho.). (3)
A generally preferred mode of operating such transmissions has been to apply an input torque to the alpha body to carry the beta body in nutation and hold the omega body against rotation (.omega.=0). The beta body is linked with an output shaft rotatable on the first axis by gearing having a ratio factor (k) which theoretically may be of any value and also may be made either positive or negative depending on the particular gearing arrangement used. In light of the foregoing, where .theta. is unit output speed and taking into account the gearing ratio (k), the output/input speed ratio of the unit is determined by an equation: EQU .theta./.alpha.=1-k.rho.. (4)
A principal advantage of operating in the mode represented by equation (4) is that the physical parameters of such I.V. transmissions readily accommodate a range of values for the function (k.rho.) which permit a continuously variable output/input speed ratio range of from zero to 1 (1.0&lt;k.rho.&lt;2.0). Also, this range may be shifted to include an output reversal through zero merely by selecting a gear ratio (k) so that the function (k.rho.) brackets a numerical value of 1 (e.g. 1.5&gt;k.rho.&gt;0.7).
In transmissions which operate to vary speed ratios in accordance with equation (4), the second bracketed function on the right side of equation (2) will vary with the speed .beta. at which the beta body rotates about the second axis in a fixed frame of reference and as determined by the variable factor .rho.. Since the factors .beta. and .rho. are determinative of transmission output speed, a fixed counterweight system is, therefore, effective to balance that portion of the inertial couple represented by the second function to the right of equation (2) at only one output speed.
The result of any imbalance between the inertial couple developed in the beta body and a counterbalancing couple developed by fixed counterweights on the alpha body is a net nutational couple which behaves physically in a manner resembling a pair of axially spaced, rotatable weights displaced eccentrically from the rotational axis thereof at an angle of 180.degree.. Such a net nutational couple is a source of vibration particularly at high output speeds.
The vibration resulting from the aforementioned net nutational couple has been reduced heretofore by appropriate fixed counterweight designs so that the vibration can be tolerated in many applications where the transmission is capable of being supported in a manner to damp the vibrations or where output speeds are relatively low. In many applications where the advantages of operation to vary speed ratio in accordance with equation (4) are desirably combined with reduced or no vibration, further provision for counterbalancing must be made.